Ambiguous controls on simulated diazotrophs in the world oceans

Nitrogen fixers, or diazotrophs, play a key role in the nitrogen and carbon cycle of the world oceans. Diazotrophs are capable of utilising atmospheric dinitrogen which is a competitive advantage over generally faster growing ordinary phytoplankton in nitrogen-depleted conditions in the sun-lit surface ocean. In this study we argue that additional competitive advantages must be at play in order to explain the dynamics and distribution of diazotrophs in the global oceans. Backed by growing published evidence we test the effects of preferential grazing (where zooplankton partly avoids diazotrophs) and high-affinity diazotrophic phosphorus uptake in an Earth System Model of intermediate complexity. Our results illustrate that these fundamentally different model assumptions result in a very similar match to observation-based estimates of nitrogen fixation while, at the same time, they imply very different trajectories into our warming future. The latter applies to biomass, fixation rates as well as to the ratio of the two. We conclude that a more comprehensive understanding of the competition between ordinary and diazotrophic phytoplankton will reduce uncertainties in model-based projections of the oceanic N cycle.

The ocean component of UVic 2.9 is based on a three-dimensional primitive-equation model 15 . The vertical discretization of the ocean comprises 19 levels and increases gradually from 50 m at the surface to 500 m at depth. The vertical background mixing parameter, κ h , is 0.15 cm 2 s −1 throughout the water column. In the Southern Ocean (south of 40 • S) this background diffusivity, κ h , is increased by 1.0 cm 2 s −1 . An anisotropic viscosity scheme 16 is implemented to improve the equatorial circulation 17  In the following, we present a choice of details relevant for the simulated dynamics of diazotrophs (relevant model parameters are listed in Tab.S1 while relevant model data misfits are listed in Tab. S2): phytoplankton growth is generally controlled by the availability of light and nutrients (here, nitrate, phosphate and iron, where the latter is parameterized by a prescribed mask, rather than explicitly resolved). Phytoplankton blooms are terminated by zooplankton grazing, once the essential nutrients are depleted and the related reduction in phytoplankton growth does not longer keep up with the grazing pressure, that has built up during the bloom. For ordinary phytoplankton the maximum potential growth rate is where k F e =0.1 mmol F e/m 3 is the half-saturation constant for iron (Fe)-limitation and a = 0.6 d −1 determines the maximum potential growth rate at an ambient temperature T = 0 • C.
For diazotrophs the formulation of the maximum potential growth is similar, but diazotrophs are permanently disadvantaged in nitrate-replete waters by C d = 0.3. In addition, growth is stalled in waters colder than 15 • C: The actual growth rate of non-diazotrophic phytoplankton, J O , is, in case of low irradiance (I) and/or nutrient depleted conditions, the maximum potential rate J max o reduced by the following implementation of Liebig's law of the minimum: where k N and k P are the half saturation constants for N O 3 and P O 4 , respectively.
The actual growth rate of diazotrophs, J D , is similar but it is not affected by nitrate deficiency: The light-limited growth J IO and care both determined by: The initial slope of the P-I curve (α) is set to 0.1 (W/m 2 ) −1 d −1 . Diazotrophs take up available nitrogen following: where P D denotes the biomass of diazotrophs (in units molN/m 3 ). When no or not enough bioavailable N is available, nitrogen fixation tops the respective N pool up to a Redfield-ratio of N:P=16. Note that the above formulation differs slightly from the original formulation 4 which reads: Our minor change ensures a more realistic behavior where no nitrogen is fixed under nitratereplete conditions. When applied to the reference model version, the difference to the original simulation turned out to be negligible.
The reference version of our Uvic 2.9 is an implementation of the preferential grazing paradigm 4 . The grazing is characterized by a multiple-prey Holling II functional response that assigns preferences for different types of prey (phytoplankton, detritus and zooplankton). The rate of grazing on phytoplankton is determined by: with a maximum growth rate µ max = 0.4 d −1 and Z referring to the biomass of zooplankton. Grazing on ordinary phytoplankton, P O , is calculated by setting θ = θ o = 0.3. Grazing on diazotrophs, P D , is calculated with a lower grazing preference θ = θ d = 0.1.

Model setups and specific assumptions
The implementations of the two competitive advantages on the ecological niche of diazotrophs investigated in our study refer to specific parameter settings in our model. The selective grazing paradigm is implemented by adjusting the grazing preferences for diazotrophs and ordinary phytoplankton, θ d and θ o , with the additional constraint θ d +θ o = 0.4. In addition, C d is varied in attempt to minimize the misfit to observations. In total, we explored 24 combinations of the parameters θ d , θ o and C d . In the following, GRAZ refers to the most realistic member of the set of 24 that outperforms the reference version (cf., Tab. S1 & S2). Note that also the original simulation 4 uses selective grazing but is not optimized towards a nitrogen fixation estimate (which is necessary for our purposes, i.e., the comparison with the second mechanism). Preferential grazing is a relatively common assumption in biogeochemical models and e.g. related to the fact that some diazotroph species can be inedible or toxic to zooplankton 18,19 .
The second paradigm, represented by OLIGO, assumes that diazotrophs can cope better with oligotrophic conditions than ordinary phytoplankton. This paradigm is based on the the idea put forward by foregoing studies 20 that diazotrophs can allocate relatively more N to the P-uptake machinery than ordinary phytoplankton under nutrient-depleted conditions. This is of relevance because P-depletion demands greater N investments into nutrient uptake machinery 21,22 . This paradigm is implemented by (1) setting equal grazing preferences for diazotrophs and ordinary phytoplankton conforming with the additional constraint of θ d + θ o = 0.4 and (2) tuning the half-saturation constant for phosphate limitation of diazotrophs k d P (where the values considered are smaller than the original value). Again, C d is varied in addition to minimize the misfit to observations. In total we explore 24 values for k d P and C d . The respective parameter ranges are listed in Tab. S2 and were designed to ensure that diazotrophs have an additional competitive advantage over other phytoplankton in our model. This sets a limit on preferential grazing of 0.2 and 0.044 for the half-saturation constant for PO 4 for diazotrophs. The half saturation constant can not reach zero. Making selective grazing even stronger than in our study leads to an unrealistic die out of other phytoplankton (e.g. in the upwelling region of the equatorial Pacific). The same holds when increasing C d above 0.6. In the following OLIGO refers to the most realistic member of the set of 24 that, according to the root mean squared error (RMSE) of simulated nitrogen fixation relative to the considered recent estimate 2 .
For the model assessment and the parameter choices we consider climatological annual means in quasi-equilibrium under preindustrial CO 2 emissions and exclude solutions with very low biomass of diazotrophs (below an integrated value of 10 T g C). Note, that, while using the RMSE is common 23,24 , any choice of a model-data misfit metric inevitably adds a subjective element because the respective choice may well affect the results of the optimisation procedure 25,26 . In addition to the two optimized model setups described above, we performed two control simulations: the setup CONTR assumes the same grazing pressure on diazotrophs and other phytoplankton and also uses the same PO 4 half-saturation constants for dizotrophs and ordinary phytoplankton. The respective parameter values are listed in Tab. S1. Note that C d in CONTR has been set to match GRAZ and OLIGO. The final setup DECAY is identical to CONTR apart from denitrification being set to zero in this model setup.
Table S1: Relevant model parameters in the model version CONTR and the setups GRAZ and OLIGO. Bold values refer to parameters obtained during tuning exercises. Note that θ o has been calculated with the equation θ d + θ o = 0.4. The last column gives the ranges, in which the parameters were varied to minimize the misfit to the independent nitrogen fixation estimate 2 . The values for GRAZ and OLIGO refer to the respective "best" simulations after the parameters were varied independently.

Param. Description
Units CONTR GRAZ OLIGO Range

Supplementary Figures
The supplementary Figure S1 shows